Flat substrates, such as semiconductor wafers, are stressed during certain processing steps, e.g., depositing or etching thin films. Stress in deposited layers can warp the substrate, which can adversely affect subsequent process steps, device performance, reliability and line-width control. Thus, it is desirable to measure the radius of curvature of a substrate as well as measure the stress on a substrate that is associated with a processing step.
There are many measurement tools available for measurement of the radius of curvature and analysis of the stress associated with certain processing steps on substrates. Most of the available tools for the semiconductor industry use a laser displacement sensor to measure the radius of curvature and to monitor the change in radius of curvature of the wafer before and after the processing step. Generally, radius of curvature is used to describe the bow of the substrate over a larger scale, e.g., the diameter of the substrate.
A laser displacement sensor relies on the reflectance of a laser beam from the surface of the sample to quantify the change in angle of incidence of the beam with respect to the wafer. This information can be transformed into an average radius of curvature for an entire diameter of a wafer or an average radius of curvature for a fraction of a diameter allowing the calculation of stress as a function of position along the diameter. This measurement can be repeated at a number of locations within a diameter and at a multitude of diameters to create a map of the stress over an entire wafer.
During the radius of curvature measurement, the substrate is typically placed on a stress-free chuck. FIG. 1 is a perspective view of a conventional stress-free chuck 10 with three pins 12 that support a substrate 14 (illustrated with broken lines). FIG. 2 is a side view of chuck 10 and pins 12 support substrate 14, which has been deposited with a thin film 16. The bowing of substrate 14 is shown greatly exaggerated in FIG. 2 for illustrative purposes. The radius of curvature of the substrate 14 prior to and after the deposition of the film 16 can be compared and converted into the stress in the film σ using the bending plate method as follows:
                    σ        =                              1            6                    *                      [                                          1                                  R                  post                                            -                              1                                  R                  pre                                                      ]                    *                      E                          (                              1                -                n                            )                                *                                    t              s              2                                      t              f                                                          eq        .                                  ⁢        1            where σ is the stress in the film, R is the radius of curvature (pre and post deposition), E is Young's modulus, n is Poisson's ratio, ts is the substrate thickness, and tf is the film thickness.
As can be seen in equation 1, in order to determine the stress in the film, the thickness of the film must also be measured. Thickness measurements are preferably made on a flat substrate, e.g., with the substrate held flat with a vacuum chuck. Thus, thickness measurements are sometimes made at a separate metrology station than the radius of curvature measurement, which uses a stress-free chuck.
In order to increase throughput, however, the thickness of the film on the substrate is sometimes measured while the substrate is on the stress-free chuck 10. As illustrated in FIG. 3, the bowing of the substrate 14 (only a portion of which is shown) will cause the light 18 to be incident at a non-normal angle θ, which is dependent on the amount of bowing of the substrate and, thus, is an uncontrolled parameter. Accordingly, the angle of incidence of the light from the metrology instrument must be included as fit parameter, which slows calculation and is somewhat inaccurate. Additionally, while the substrate 14 is held on the stress-free chuck 10, the substrate 14 is subject to vibrations, which can create errors in the thickness measurement.
Thus, what is needed is an improved system that can accurately hold and measure a substrate in multiple orientations, i.e., flat and stress-free without using separate metrology stations.